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comment Draw a non-planar graph whose complement is a non-planar graph
UG is the Utility Graph. See en.wikipedia.org/wiki/Complete_bipartite_graph#/media/…
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accepted Draw a non-planar graph whose complement is a non-planar graph
Jul
27
awarded  Teacher
Jul
27
answered Draw a non-planar graph whose complement is a non-planar graph
Jun
2
comment Draw a non-planar graph whose complement is a non-planar graph
This answer is correct and easy to follow if you already know about Euler's formula. The text I am reading introduced the concept of planar and nonplanar graphs before Euler's formula. So, at that time, it was hard for me to follow your suggestion.
Jun
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awarded  Scholar
Jun
2
accepted Counting clarification
May
28
answered Counting clarification
May
28
comment Counting clarification
Thanks for the answers, André Nicolas and N. F. Taussig. I found a simpler way of counting the even numbers. First count the odd numbers. There are (3) ways of choosing the unit's place. There are (5) ways of choosing the thousand's place(0 cannot be used and one already chosen in unit's place). There are (5) ways to choose the hundred's place.(2 already chosen). Similarly, there are (4) ways to choose the ten's place. Therefore, there are (5)(5)(4)(3) odd numbers. ie, 300 odd numbers. Total even numbers = 720-300 = 420. Is this valid method of counting?
May
27
asked Counting clarification
May
21
comment Draw a non-planar graph whose complement is a non-planar graph
Add this an answer, I will accept it. I returned to doing graph theory again and now this idea appears so simple. To quote an example, I drew UG and added six more isolated vertices. Now, in G' K6 is a subgraph and therefore G' is nonplanar.
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29
awarded  Supporter
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27
awarded  Editor
Jan
27
revised Draw a non-planar graph whose complement is a non-planar graph
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Jan
16
awarded  Student
Jan
16
asked Draw a non-planar graph whose complement is a non-planar graph